I was an ER tech for 6 years - here's my take.
It really depends on the hospital like everyone else said. I'll qualify that though - it has been my experience that the bigger the hospital, the more training you will generally be required to have. If you don't want to go through the process of getting an EMT or other cert, I'd say stick to smaller (usually community-type) facilities. No matter where you go, though, you WILL be required to get CPR cert'd (almost always AHA BLS for Healthcare Provider).
Personally, though I think if you are willing to get some sort of cert, I think an EMT would be much more useful in the ER setting than a CNA - the scope of practice is wider and the knowledge base is much more useful in terms of you understanding what's going on with the patients.
Many times, also, without an EMT, you may be restricted to clerical / unit secretary type jobs.
And to dispel what appears to be a misconception on this thread - EMT'S ARE NOT CONFINED TO AMBULANCES.